Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Calculus, Linear Algebra, Physics

This course intends to provide the theoretical and practical bases for the comprehension of the main methods and applications of the basic sciences to the conception and analysis of civil and enviromental engineering structures. Specifically, the course deals with the methods of analysis of isostatic and hyperstatic structures, the fundamental principles of continuum mechanics, elasticity and elastic beams. Moreover, we provide the skills to solve strength and deformability evaluation problems for beams structures.

In order to tackle the topics related to structural design and analysis, the student will acquire the competences to autonomously identify and solve problems. These competences will provide the student with the knowledge that will be useful for professional activities (structural design, management and organization) in freelance, industry or public administrations career profiles, thanks also to the interaction with other civil and environmental engineering experts.

The presented theory and the discussed problems represent a basic theoretical tools in the design of any structural system. These concepts are essential in order to interpret, analyze, model and solve more complex problems related to structural analysis.

Vector spaces. Scalar and vectorial products. Tensor spaces. Identity tensor. Transpose. Symmetric and skew-symmetric tensor: axial tensor. Orthogonal tensors. Kinematics. Deformation and deformation gradient. Deformations of line, surface and volume elements. Polar decomposition theorem. Kinematics of rigid bodies: degrees of freedom. Spin Tensor and angular velocity. Poisson formula. Plane rigid motion. Constraint: lagrangean coordinates. Multiple constraints. Statically determinated, undeterminated and impossible systems. Rigid body statics: internal actions in rigid systems. Work, power and energy. Force and couplke resultants. Virtual power principle. Static balance laws. Reactive forces in constrained rigid systems. Reactive forces in statically determinated rigid systems. Reactive forces and equilibrium configurations in statically impossible rigid systems. Statics of rods: internal actions, balance laws and boundary conditions. Internal action diagrams. Plane rods: archs and straight rods. Rods kinematics: kinematical descriptors, deformations measures, compatibility equations. Kirchhoff's rod. Constitutive relations: linearly elastic rods. Virtual works, energetics and variational formulations. Minimum principles. Hyperstatic plane frames; the Müller-Breslau equations as a consequence of Complementary nergy minimum principle. Tridimensional linear elasticity. Kinematics: displacement and strain. The infinitesimal strain tensor. Statics: the notion of stress. Cauchy's theorem. Virtula works for defromable systems. Linear isotropic materials. The Saint-Venant's problem for isotropic solids. The Clebsch's solution. Yield criteria . Stability of Euler beams.

The final test consists of a written test and an oral colloquia. The written test requires the study of a simple hyperstatic plane frame.

The written test must verify the ability to resolve a statically-indeterminate plane truss, determining also the displacements of a given section and performing the safety analysis of another section. The diagrams of the stress characteristics must be correctly drawn and from the data provided in the text the displacement or rotation of a section must be correctly evaluated. The ideal Huber-Von Mises tension compatible with the admissible one must be also evaluated for a section In the oral test must verify the ability to solve problems of a theoretical or applicative nature by starting from the equations of mechanics of deformable bodies. It could also require proofs of theorems or deductions of equations, focusing more on the deductive aspects rather than on mnemonic.

In the written test the relevance of the obtained results with the solution is checked; in the oral test both the knowledge of the topics and the capability to develop solutions to proposed problem are checked

For the written exam is admitted only the positive result associated with the determination of the exact solution. For the oral exam grade is assigned by taking into account the topics knowledge, the capability to apply these knowledges to solve examples and the smartness and neatness of language

F. Davì, Note di Scienza delle Costruzioni, 2013 (free downloadable from University official Webpage) P. Podio-Guidugli, Lezioni di Scienza delle Costruzioni, Aracne Editrice, Seconda Edizione 2009 L. Gambarotta, L. Nunziante ed A. Tralli, Scienza delle Costruzioni, McGraw-Hill, Terza Edizione 2011. C. Comi e L. Corradi Dell'Acqua, Introduzione alla meccanica strutturale, McGraw-Hill, 2003. F.P. Beer, E.R. Johnston Jr. e J.T. DeWolf, Meccanica dei solidi, McGraw-Hill, Terza Edizione 2006

- Ingegneria Civile e Ambientale (Corso di Laurea Triennale (DM 270/04))

**Università Politecnica delle Marche**

P.zza Roma 22, 60121 Ancona

Tel (+39) 071.220.1, Fax (+39) 071.220.2324

P.I. 00382520427